3. Kyle and Michael a rup a lap around a track. Kyle gets a 50 a meter head start and runs 3 meters
per
second. Michael runs at a speed of 4 meters per second. How long will it take for Michael
to reach Kyle?

Test the hypothesis step of the scientific method is he performing.

Making conjectures (hypothetical explanations) is a step in the scientific method. Predictions are then derived from the hypotheses as logical conclusions, and experiments or actual observations are conducted based on those predictions.

Since at least the 17th century, the scientific method—an empirical approach to learning—has guided the advancement of science. Since one's interpretation of the observation may be distorted by cognitive presumptions, it requires careful observation and the application of severe skepticism regarding what is observed.

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The probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring, this statement is false.

The union of two or more sets refers to the set with all the elements belonging to each set. An element is said to be in the union if it lies to at least one of the sets.

The intersection of two or more sets refers to the set of elements universal to each set. An element is in the intersection if it occurs in all of the sets.

The event that both A and B occur is the intersection of the events A occurs and B occurs. As such, it is a subset of each and cannot, therefore, have a larger probability than either one individually.

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Answer:

g(x) = –log2(x + 2)

Step-by-step explanation:

got it right on the assignment

The function that represents the function f(x) is reflected over the x-axis and shifted left by 2 units will be g(x) = - log 2x + 4.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given below.

f(x) = log 2x

The function is reflected over the x-axis, then the function will be

h(x) = - log 2x

And shifting left by 2 units, then replace x with (x + 2). Then the equation will be

g(x) = - log 2(x + 2)

g(x) = - log 2x + 4

The function that represents the function f(x) is reflected over the x-axis and shifted left by 2 units will be g(x) = - log 2x + 4.

The graph is given below.

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The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.

Given,The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam.

For a particular type of wood, the value of S of a beam is proportional to the product of the width and the square of the depth of its cross-section.

The strength of an oak beam is 69, when the beam is 7 inches wide and 3 inches deep.Thus, we can conclude that k, a constant of proportionality exists, such that: S=k(W x D²), where W is the width, D is the depth of the rectangular cross-section and S is the strength of the beam.

Let's use this to calculate k: When the beam is 7 inches wide and 3 inches deep, S=69. Thus, we get:k = S/W x D²=69/(7 x 3²)=1.

Thus, the equation for S becomes:S = W x D²The radius of the oak tree is 28/2 = 14 inches and the beam must be 14 inches wide.

This implies that the rectangular cross-section of the beam must be square (or the largest rectangular cross-section is a square). Let the side of the square cross-section be x.

Thus, we can write:S = x²Diameter, d = 28 inches => radius, r = 14 inchesWe need to determine the depth of the beam. The depth of the beam is half the height of the cylindrical log from which the beam is cut. The cylindrical log has a diameter of 28 inches. The beam has a width of 14 inches.

The largest rectangular cross-section is a square with sides of length x. This cross-section can be obtained by cutting the log at a height of x/2 from its center.Since the diameter is 28 inches, the radius is 14 inches. The height at which the beam is cut is h = 14 - x/2.

Thus, the depth of the rectangular beam cut from the cylindrical log is given by: D = 2(h) = 2(14 - x/2) = 28 - x.Using the relationship S = W x D² with S = 69, W = 14 and k = 1, we can write:x² (28 - x)² = 69Simplifying the above equation,x⁴ - 56x³ + 784x² - 69 = 0.

Using polynomial long division, we get:(x² + 16x - 69)(x² - 40x + 1) = 0The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.Therefore, the  answer is (b) S = 2231.

The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam. Let the side of the square cross-section be x. Thus, we can write:S = x²Diameter, d = 28 inches => radius, r = 14 inches. Using the relationship S = W x D² with S = 69, W = 14 and k = 1, we can write:x² (28 - x)² = 69.The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.

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The simple interest on 17,000 loan for 10 years will be 11,900

Solution:

As we know,  simple interest is the interest amount for a particular principal amount of money at some rate of interest.

Here given ,

Principle (P) = 17,000

Rate of interest (R) = 7%

Time (T)= 10 years

Simple Interest = (RxRxT)/100

Therefore,

S.I. = ( 17,000 x 7 x 10 ) / 100

     = 11,900

Hence,

The simple interest at the end of 10 years will be 11,900

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lim n → [infinity] (n^2+2n+1)/n^4 * 3^n = 0 (by the ratio test), we can conclude that the limit lim n → [infinity] (a_n+1 / a_n)^3/2 = 1. Therefore, the series converges by the Ratio Test.

To determine whether the series [infinity] n = 1 (−1)n − 1 3n 2nn3 converges or diverges, we can use the Ratio Test.

Using the Ratio Test, we calculate:

lim n → [infinity] |a_n+1 / a_n|

= lim n → [infinity] |(-1)^(n+1) * 3^(n+1) * 2n * (n+1)^3 / (n^3 * (-1)^n * 3^n * 2n)|

= lim n → [infinity] |(3/2) * (n+1)^3 / n^3|

= lim n → [infinity] (3/2) * [(n+1)/n]^3

= (3/2) * lim n → [infinity] (1 + 1/n)^3

= (3/2) * 1

= 3/2

Since the limit of |a_n+1 / a_n| is less than 1, by the Ratio Test, the series converges absolutely.

To identify a_n, we can rewrite the given series as:

∑ (-1)^n-1 * (2n/n^3) * (1/3)^n

Therefore, a_n = (-1)^n-1 * (2n/n^3) * (1/3)^n.

To evaluate the limit lim n → [infinity] (a_n+1 / a_n)^3/2, we can simplify the expression as follows:

lim n → [infinity] (a_n+1 / a_n)^3/2

= lim n → [infinity] |-1 * (2(n+1)/(n+1)^3) * (n^3/(2n)) * (3/1)^n|^3/2

= lim n → [infinity] |-2/3 * (n^2+2n+1)/n^4 * 3^n|^3/2

= |-2/3 * lim n → [infinity] (n^2+2n+1)/n^4 * 3^n|^3/2

Since lim n → [infinity] (n^2+2n+1)/n^4 * 3^n = 0 (by the ratio test), we can conclude that the limit lim n → [infinity] (a_n+1 / a_n)^3/2 = 1. Therefore, the series converges by the Ratio Test.

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Step-by-step explanation:

13) 4x-22+x+11+10x-4 =180

15x=195

x=13

<P=(10(13)-4)=126

<Q=(4(13)-22)=30

<R=13+11=24

Answer:

Human activities such as driving cars, and working at factories contribute to global warming significantly because burning fossil fuels in cars releases carbon dioxide, which is the largest source of greenhouse gas emissions in the U.S. and as these gases build up, they trap heat in the atmosphere, causing climate change.

Answer:

.04 miles

Step-by-step explanation:

1 meter = 0.0006213712 miles

59 meters x 0.0006213712 miles = 0.0366609008 miles

Round to nearest hundredth: .04 miles

Answer:

nudaw HAHABSASASNA

Step-by-step explanation:\(x^{2} g\)

hggggguuuuugs berte bhu jira yuwa

Answer:

EB

Step-by-step explanation:

all of the other lines are either diagonal on a 2D plane, or they are regular lines that make up the rectangular prism.

Answer:

think it is 183 - π(6)2(12) or J because it is the closes

Volume of packing materials = Volume of box - volume of cylinder

Since the box has same shape as a cube, the volume = L3

Where L is the lenght of the box

Volume of a right circular cylinder = πr2h

where r is the radius and h is the height

Volume of packing materials = L3 - πr2h

hope this will or can (even maybe) helps

The number of cubic inches of the box which is filled with packing material is 5194.83 cubic inches approx.

Volume is the measure of the 3 dimensional space occupied by the object.

If the filled substance occupies almost the whole inside of the considered object, then the volume of the material in the object is the space it occupies, which is equal to the space inside that box, which is its interior volume.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

\(V = \pi r^2 h \: \rm unit^3\)

For the given case, the packing material occupies whatever space is left in the box, after that cylinder is putted inside of the box.

Volume of the packing material filled in the box = Volume of the remaining space of the box after cylinder is placed = Volume of box - Volume of the cylinder in the box

Now, volume of the box = cube of its side length (as box is cubic, so we used formula for volume of a cube which is its side cubed),

Volume of the box = \(18^3 = 6552\) cubic inches

Volume of cylinder =

\(V = \pi r^2 h \: \rm unit^3 = \pi \times (6)^2 \times 12 = 432\pi\\ V \approx 1357.17 \: \rm inch^3\)

Thus, volume of the remaining space = \(6552 - 1357.17 = 5194.83 \: \rm inch^3\)

This is the amount of space left in the box, the same amount of space the packing material will occupy.

Thus, the number of cubic inches of the box which is filled with packing material is 5194.83 cubic inches approx.

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It would take approximately 19.65 years for an investment of $100,000 at a 7% annual interest rate to grow to $500,000. Rounded to two decimal places, the answer is 19.65 years.

To determine the number of years it will take for an investment of $100,000 at a 7% annual interest rate to grow to $500,000, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment ($500,000)

P = the initial principal amount ($100,000)

r = the annual interest rate (7% or 0.07)

n = the number of times that interest is compounded per year (assuming annually, so n = 1)

t = the number of years

Plugging in the values we know, we get:

$500,000 = $100,000(1 + 0.07/1)^(1*t)

Dividing both sides of the equation by $100,000 and simplifying:

5 = (1.07)^t

To solve for t, we can take the logarithm of both sides:

log(5) = log[(1.07)^t]

Using logarithmic properties, we can bring down the exponent:

log(5) = t * log(1.07)

Finally, we can solve for t by dividing both sides by log(1.07):

t = log(5) / log(1.07)

Using a calculator, we find:

t ≈ 19.65

Therefore, it would take approximately 19.65 years for an investment of $100,000 at a 7% annual interest rate to grow to $500,000. Rounded to two decimal places, the answer is 19.65 years.

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Given:

Rita covered 1 mile in 15 minutes.

She covered 3 miles in 30 minutes.

To find:

The rate at which she is riding.

Solution:

Let y be the number of miles covered in x minutes.

Rita covered 1 mile in 15 minutes. So, the point is (15,1).

She covered 3 miles in 30 minutes. So, the point is (30,3).

Slope of the line:

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

\(m=\dfrac{3-1}{30-15}\)

\(m=\dfrac{2}{15}\)

Therefore, she is riding \(\dfrac{2}{15}\) miles per minute.

To evaluate the limit using continuity, we need to consider the intervals on which both the numerator and denominator are continuous. The numerator 12Vx is continuous for all values of x. The denominator 12+x is continuous and nonzero for all values of x except when x = -12.

Continuity is a property that ensures a function is well-behaved and does not have any abrupt jumps or holes in its graph. To evaluate the limit, we need to ensure that both the numerator and denominator of the expression are continuous on the interval in question. In this case, the numerator 12Vx is a simple function and is continuous for all values of x. There are no restrictions or exceptions.

The denominator 12+x is also continuous for all values of x except when x = -12. At x = -12, the denominator becomes zero, which would result in an undefined value for the fraction.

Therefore, the numerator is continuous on the entire real number line, and the denominator is continuous and nonzero for all values of x except x = -12.

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The length of the rectangular  playground is 241.86 foot.

Given that area of rectangle is 19,500 sq.ft and length of rectangle is three times its width.The area for rectangle is given by formula: A=LW.

Now according to the given condition, L= 3W. Further we'll solve by putting L= 3W in the formula for rectangle.

A=LW

As given A= 19,500 sq.ft and considering L=3W,

19,500 = 3W*W

19,500 = 3W^2

∴ W^2 = 6500

∴ W = \(\sqrt{6500}\)

∴ W = 80.6225 ft. ≈ 80.62 ft.

Now putting the value W = 80.62 in equation L =3W,

L = 3* 80.62

L = 241.86 ft.

The length of the rectangular playground is 241.86 foot.

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1. The point estimate for the mean of the population is 79.

2. The point estimate for the standard deviation of the population is 27.1.

3. The point estimate for the variance of the population is 735.61.

4. The point estimate for the proportion of all students who passed the course is 80%.

Answer:y=-1/3x+10/3

Step-by-step explanation:

If the line is perpendicular it means the slope is the negative reciprocal of the line. The slope of line r should be -1/3. Now the equation for line r is: y=-1/3x+b. We then can plug in values: 3=-1/3(1)+b=3=-1/3+b, b=10/3. The equation is: y=-1/3x+10/3.

Answer:

Step-by-step explanation:

y = 3x - 2

slope m1 = 3

Slope of line r = -1/m1 = -1/3

Equation of line in slope intercept form:  y= mx +b

\(y=\dfrac{-1}{3}x+b\)

Plugin x = 1 and y= 3 in the above equation.

\(3=\dfrac{-1}{3}*1+b\\\\3= \dfrac{1}{3}+b\\\\\\3+\dfrac{1}{3}=b\\\\\dfrac{9}{3}+\dfrac{1}{3}=b\\\\\\b =\dfrac{10}{3}\)

Equation of line r :

\(y = \dfrac{-1}{3}x + \dfrac{10}{3}\)

t is 1.383.

HTML tags cannot be used on the platform. However, the solution to the question is as follows:

Step 1: We must first find the t value such that 0.1 of the area under the curve is to the right of t.

For the given problem, the area to the left of t is 1 - 0.1 = 0.9.The value of t can be found using a t-table. This will give us the corresponding t-value for 0.9 area to the left of t.

Step 2: Assuming the degrees of freedom equals 9, select the t-value from the t table.Since we have 9 degrees of freedom and we need to find the t-value for 0.9 area to the left of t, we must look at the row that corresponds to 9 degrees of freedom in the t-table. In that row, we must look for the column that has a value closest to 0.9.

The t-value in that column will be the required value of t. The t-value that has a 0.9 area to the left of it is 1.383.So, the value of t such that 0.1 of the area under the curve is to the right of t is 1.383.

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A period is the difference in x over which a sine function returns to its equivalent state and the amplitude is A/5.

Amplitude:

The amplitude of a periodic variable is a measure of its change over a period of time, such as a temporal or spatial period. The amplitude of an aperiodic signal is its magnitude compared to a reference value. There are various definitions (see below) of amplitude, which is any function of the magnitude of the difference between the extreme values ​​of a variable. In the previous text, the phase of a periodic function is called the amplitude.

                       X = A sin (ω[ t - K]) + b

A is the amplitude (or peak amplitude),

x is the oscillating variable,

ω  is angular frequency,

t is time,

K and b are arbitrary constants representing time and displacement respectively.

According to the Question:

An equation does not have an amplitude. This "equation" represents the formula of a vibration, and was better written as:

X= A/5* sin(1000.t + 120)

These oscillations have a certain amplitude. X values ​​can vary from minimum to maximum. Normally, the stop position of the oscillation is X=0. In this case, we can see that the maximum occurs when the sine is +1 and the minimum occurs when the sine is -1.

For theses cases X= A/5 respectively -A/5.

Therefore,

The amplitude is A/5.

For formulas of this type, the term in front of the sinus (or cosine) is equal to the amplitude.

Complete question:

Can I find the amplitude of this equation? A/5 *